LloydKMeans.java

package graphtea.extensions.algorithms;

import graphtea.graph.graph.GPoint;
import java.util.ArrayList;
import java.util.Arrays;

/**
 * http://frodriguez.webs.com/Java%20Algo/kmeans.txt
 *
 * Lloyd's Algorithm - A greedy approximation to the kmeans clustering problem (NP-HARD), this is similar to
 *                     finding the centers of the voronoi cells of a tessellation that has the input points
 *                     distributed as evenly as possible throughout the cells.
 *
 * Steps:
 * 		1) It guesses an initial location for the center of each cluster
 * 		2) It assigns each input point to one cluster (the one with the closest center)
 *			3) For each cluster, move its center to the centroid of all its assigned points.
 *			4) Repeat steps 2-3 until no change occurs.
 *
 * Returns: An array of Clusters. If you need exactly k clusters you may have to run it several times since
 *          some clusters may die out during the algorithm, this shouldn't be a problem because this function
 *          usually runs very fast.
 */

public class LloydKMeans {

	public static Cluster[] cluster(GPoint[] p, int k) {
		GPoint[] center = new GPoint[k];
		int[] parent = new int[p.length];
		Arrays.fill(parent, -1);

		// find an initial "fair" placement for the k clusters
		// places them radialy around the centroid
		GPoint point = new GPoint(0, 0);
		for (GPoint aP : p) point.add(aP.x, aP.y);
		point.multiply(((double) 1) / p.length);

		for (int i = 0; i < k; i++)
			center[i] = new GPoint((int) (point.x + 100 * Math.random()), (int) (point.y + 100 * Math.random()));

		while (true) { // improve on those centers with each iteration
			boolean improved = false;

			// partition the GraphPoints into k clusters
			for (int x = 0; x < p.length; x++) {
				double bestDist = Double.MAX_VALUE;
				int inx = -1;
				for (int i = 0; i < k; i++) {
					double d = p[x].distance(center[i]);
					if (inx == -1 || d < bestDist) {
						inx = i;
						bestDist = d;
					}
				}

				if (parent[x] != inx)
					improved = true; // something was altered

				parent[x] = inx; // add GPoint to the proper cluster
			}

			if (!improved)
				break;

			// now improve by updating the center of the clusters
			GPoint[] sum = new GPoint[k];
			for (int i = 0; i < sum.length; i++)
				sum[i] = new GPoint(0, 0);

			int[] count = new int[k];

			for (int i = 0; i < p.length; i++) {

				sum[parent[i]].add(p[i].x, p[i].y);
				count[parent[i]]++;
			}

			for (int i = 0; i < k; i++)
				center[i] = new GPoint((int) (sum[i].x / count[i]), (int) (sum[i].y / count[i]));
		}

		ArrayList<Cluster> ret = new ArrayList<>();
		for (int i = 0; i < k; i++)
			ret.add(new Cluster(center[i]));

		for (int i = 0; i < p.length; i++)
			ret.get(parent[i]).addMember(p[i]);

		// remove all empty clusters (due to bad initial placement)
		for (int i = 0; i < ret.size(); i++)
			if (ret.get(i).getMembers().size() == 0)
				ret.remove(i--);

		return ret.toArray(new Cluster[0]); // the result may not have exactly k
											// clusters since some clusters may
											// have been superfluous
	}

}